The question is: can the halting problem be solved if the solver is not being assembled/emulated/generated/recreated/put your choice here/used in any form inside the analyzed function?
There is a very similar question: Is it possible to make a halting function if you don't call it on itself? but the answer for it is generally that "we don't call function rather we pass function", however, if we exclude such situations either, will it become solvable?